In circle the length of PQ = 24 inches.
What is Circle?
A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the centre. The line of reflection symmetry is formed by each line that traverses the circle. Additionally, it possesses rotational symmetry around the centre for each angle.
Since AB= 25 inches and AC = 16 inches then
=> BC = AB-AC = 25-16 = 9 inches.
∠APB is a right angle because it is inscribed in a semicircle.
The three right triangles ᐃAPB, ᐃACP and ᐃPCB are all similar
because their corresponding angles are equal. Therefore
=> [tex]\frac{AC}{PC}=\frac{PC}{BC}[/tex]
=> [tex]\frac{16}{PC}=\frac{PC}{9}[/tex]
=> [tex]PC^2 = 25*9 = 144 = 12^2[/tex]
=> PC = 12 inches
By symmetry , PC = QC then,
=> PQ = 12*2 = 24 inches.
Hence the length of PQ is 24 inches.
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The heights in cm of 5 students are :60,58,54,56,42
Find the mean deviation for the given data
Answer:
54
Step-by-step explanation:
take the average of the number given
What is the difference 2/9 -1/3
Can you help me ples
because rules are meant to be guided and I also steps for acquiring what you need
two consecutive whole numbers, each less than 20, are multiplied and the product is increased by 17. There are exactly two values of the lesser of two consecutive numbers of which the result is not a prime number. Find both values of the lesser numbers?
The two Consecutive number is 16 and 17.
What is consecutive number?
Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a 1 difference. The mean and median of a sequence of numbers are equal. If n is a number, then it follows that n, n+1, and n+2 are also numbers. Examples. 1, 2, 3, 4, 5.
Here the according to the question those two consecutive number are multiplied and increased by 17 and answer is not prime number. Now,
=> 1× 2+17 = 2+17 = 19(prime number)
=> 2×3+17=6+17=23(prime number)
=> 3×4 +17 = 12+17 = 29(prime number)
=> 4×5+17 = 20+17 = 37(prime number)
=> 5×6+17 = 30+17 = 47(Prime number)
=> 6×7+17 = 42+17 = 59(prime number)
=> 7×8+17 = 56+17 = 73(prime number)
=> 8×9+17 =72+17 = 89(prime number)
=> 9×10+17 = 90+17= 107(prime number)
=> 10×11+17=110+17 = 127(prime number)
=> 11×12+17=132+17 =149(prime number)
=> 12×13+17=156+17 = 173(prime number)
=> 13×14+17=182+17 = 199(prime number)
=> 14×15+17=210+17 = 227(prime number)
=> 15×16+17 = 240+17=257 (prime number)
=> 16×17+ 17= 272+17 = 289( not prime number)
Hence the two consecutive number is 16 and 17.
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A graphic designer wants to reproduce the
logo of a mountain-climbing club for some club stationery.
The logo is a triangle with the angles shown.
W Sheliqsiz
A. The designer wants the base to be 2 inches long. How
should the triangle be drawn?
Ci ilority Postulate help the
Timis
60°
50°
Answer: Sorry!
Step-by-step explanation:
Hello! I can help you if you can add the photo and fix the typos.
The vertices of ABC are A(3,1), B(1,5), and C(5,3). Graph the image of ABC
after a composition of the transformations in the order they are listed.
Translation: (x,y)-(x-6,y+1)
Rotation: 90° about the origin
A“= (_,_)
B“= (_,_)
C“= (_,_)
The area of rectangle ABCD exists 12 sq. units.
What is meant by vertices?A polygon's vertex is a location where the sides or edges of the item or two rays or line segments meet. Vertex is a noun, whereas vertices is the plural.
Vertices are the points at which the edges of the three-dimensional shape converge. Edges are the lines that separate two faces, while faces are flat surfaces.
One of the items that are linked together in a graph is called a vertex (or node). The terms "edges" or "links" refer to the connections between the vertices. a network with ten nodes (or vertices) and eleven edges (links).
The coordinates of point D exists (3,3).
Area of rectangle ABCD = l × b = AB × BC
On further calculation we get
Area of rectangle ABCD = 6 × 2
Area of rectangle ABCD = 12 sq. units
Therefore, the area of rectangle ABCD exists 12 sq. units.
The complete question is:
Three vertices of a rectangle ABCD are A(3,1), B(-3, -1) and C(-3, 3). Plot these points on the graph paper and find the coordinates of the fourth vertex D. Also, find the area of the rectangle ABCD.
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Suppose that sin A = 0.622. What is the value of cos A?
Answer :
0.783
Step-by-step explanation:
We know that,
sin^2 (x) + cos^2 (x) = 1
Thus,
[tex] \sin^{2} (A) + cos^{2} (A) = 1 \\ cos^{2} A =1 - sin^{2} A \\ cos^{2} A = 1 - (0.622)^{2 } \\ cos^{2} A = 1 - 0.386884 \\ cos A = \sqrt{0.613116} \\ = 0.783[/tex]
Provide the equation of all vertical line that violate the vertical line test. Please help
The vertical line that violates the vertical line test is given as follows:
x = -3.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
For the relation graphed, we have that at x = -3, there are two closed bounds of the function, meaning that the input x = -3 is mapped to multiple outputs and thus the relation is not a function.
This also means that a vertical line traced at x = -3 would cross the graph of the function at two points, thus violating the vertical line test.
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x – 6y < 12 (7, -1)
(is this a solution or not??)
Based on this inequality x – 6y < 12, the ordered pair (7, -1) is not a solution.
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
In order to determine if (7, -1) is a solution of the given linear equation, we would have to test the given ordered pair by substituting its values into the linear equation as follows;
x – 6y < 12
7 – 6(-1) < 12
7 + 6 < 12
13 < 12 (False).
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The sum of 11 and three-fourths of a number is less than 112. What are the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter, "x" as a variable and write the inequality so that the term, "x" term comes first. Where necessary, write numbers as fractions (rather than decimals)
The inequality that can be used to solve the possible values of the number is 11 + 3/4x < 112 where the number x is x < 134 2/3
How to write inequality?sum of 11 and three-fourths of a number is less than 112.
Let
The unknown number = x
11 + 3/4x < 112
Subtract 11 from both sides
3/4x < 112 - 11
3/4x < 101
divide both sides by 3/4
x < 101 ÷ 3/4
multiply by the reciprocal of 3/4
x < 101 × 4/3
x < 404/3
x < 134 2/3
Therefore, the inequality which represents the situation is 11 + 3/4x < 112.
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2x+y=32
x+3y=36
solve the equation by elmination method
Answer:
x=12
y=8
Point form: (12,8)
Step-by-step explanation:
I've done this question before
Answer:
y=8 and x=12
Step-by-step explanation:
2x+y =32
multiply by 1
= 2x+y=32
x+3y=36
multiply by 2
=2x+6y=72
2x+y=32 - 2x+6y=72
=5y/5=40/5
=y=8
2x+y=32
=2x+8=32
=2x=32-8
=2x=24
=2x/2=24/2
=x=12
Question:
(a) Find the equation for the family of linear functions with slope 2 and sketch several members of the family.
(b) Find an equation for the family of linear functions such that f(2)=1 and sketch several members of the family.
(c) Which functions belong to both families?
Slope-intercept form
Equation of slope-intercept form is given as y=mx+b where m is the slope of the line and c is the y-intercept. m is used to measure the steepness of the graph. This form is simply the method of writing the equation of a line so that the slope and y-intercept are rapidly apparent.
For a family of linear functions with slope 2, the equation is y = 2x + b, where b is the y-intercept. For a family of linear functions such that f(2) = 1, the equation is y = x + b, where b is the y-intercept. Both families of linear functions have the same equation, y = x + b, and all functions belonging to both families have a slope of 1 and a y-intercept of b.
(a) The equation for the family of linear functions with slope 2 is y = 2x + b, where b is the y-intercept. To sketch several members of the family, plot several points (x, y) with the equation, then connect the points to form a line.
(b) The equation for the family of linear functions such that f(2) = 1 is y = x + b, where b is the y-intercept. To sketch several members of the family, plot several points (x, y) with the equation, then connect the points to form a line.
(c) The equation for both families of linear functions is y = x + b, where b is the y-intercept. All functions belonging to both families have a slope of 1 and a y-intercept of b.
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Q. What angle corresponds to angle 6?
Answer:
angel 2
Step-by-step explanation:
Angle 2 corresponds to angle 6.
I collect an SRS of size n from a population and compute a 95% confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data? (a) Use a larger confidence level. (b) Use a smaller confidence level. (c) Increase the sample size. (d) Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger. (e) Nothing can guarantee absolutely that you will get a larger interval. One can only say that the chance of obtaining a larger interval is 0.05.
Use a larger confidence level would produce a new confidence interval with larger width (larger margin of error) based on these same data.
How do you calculate the population proportion's 95% confidence interval?
We must determine p′ and q′ in order to construct the confidence interval. p′ = 0.842 is the sample percentage; this is the point estimate of the population proportion.
Since CL = 0.95 is the requested confidence level, the calculation is as follows: = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) = 0.025.
What does confidence interval mean?
When you conduct your experiment again or resample the population in the same way, you may anticipate your estimate to fall inside a specific range of values a certain proportion of the time. This is known as the confidence interval.
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Norfolk Sporting Goods purchases merchandise with a catalog list price of $40,000. The retailer receives a 30% trade discount and credit terms of 2/10, n/30. What amount should Norfolk pay if paid within discount period?1. Create the table that contains the following information for the last
quarter where data required for this exercise is available.
Please note that using the data for previous years and/or previous
estimates will produce grade zero for this part of the project.
Omit the intermediate lines found in Tables 7 and 8 on the web site.
Gross domestic product
Gross national product
Net national product (you should calculate it as Gross national product minus
Consumption of fixed capital)
National income
Personal income
Personal Disposable Income
Personal Savings
Present the information that you received in your project.
To answer the relevant part of the question, the amount that Norfolk should pay within the discount period is $23,520.
What is the discount period?The discount period is based on the credit terms.
For instance, 2/10, n/30 show the discount and credit terms. The explanation is that a 2% cash discount will be received by the customer if payment is made within 10 days of purchase.
Furthermore, the customer's credit period expires after 30 days. Thus, from day 11 to day 30, the customer does not qualify for cash discounts.
The catalog list price = $40,000
Trade discount = 40%
Discounted price = $24,000 ($40,000 x (1 - 40%)
Cash discount = $480 ($24,000 x 2%)
Cash payment = $23,520 ($24,000 - $480)
Thus, Norfolk Sporting Goods will pay $23,520 if it utilizes the discount.
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Please help!!! Thx so much!!!!!
Answer:
AB = 49
ABC = 253
BAC = 156
ABC = 311
Step-by-step explanation:
The whole circle is 360
360 - 107 - 49 = 204
We now know the measurement of the 3 sections shown.
AB = 49
ABC = 49 + 204 = 253
BAC = 107 + 49 = 156
ACB = 107 + 204 = 311
A rectangular paperboard measuring 26 in long and 20 in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed?
The perimeter of a two-dimensional shape is the distance around the shape. In this case, the paperboard has a semicircle cut out of it, so the perimeter of the paperboard that remains after the semicircle is removed is the distance around the remaining rectangular shape.
To calculate the perimeter of the remaining rectangular shape, you can use the formula: 2(length + width) = 2(26 in + 20 in) = 2(46 in) = 92 in.
It is important to note that the perimeter is a measure of the distance around a two-dimensional shape and it doesn't take into account the area inside the shape. Also it is measured in units, in this case inches.
I hope this helps :)
P( – 3, – 5) after a reflection over the y-axis.
Answer: 3,-5
Step-by-step explanation:
Answer: (3, -5)
......................................
For the function ƒ(x) = 2 (x − 10)² + 6, find ƒ−¹(x).
For the function ƒ(x) = 2 (x − 10)² + 6 then F⁻¹ = [tex]\frac{x- 6}{2}[/tex] + 10 is the inverse of the given functions.
Calculating the problem:y = [tex]\frac{x - 6}{2}[/tex] + 10
F⁻¹ = [tex]\frac{x -6 }{2}[/tex] + 10
Inverse functions:A function that is capable of reversing into another function is referred to as an inverse function or anti function. Simply put, if a function is denoted by "f" or "F," then the inverse function is denoted by "f-1" or "F-1." The inverse function returns the original value for which a function provided the output.
If any function "f" takes x to y, then the inverse of "f" will take y to x. A function that consists of its inverse retrieves the original value when considering functions, where f and g are inverses, and f(g(x)) = g(f(x)) = x. Then, the opposite of f(x) is g(y) = (y-5)/2 = x.
How is the inverse of a function or relationship determined?The equation of the inverse relation can be obtained by substituting every y in the equation for every x in the equation that describes the relation between the variables x and y.
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A coffee machine dispenses coffee into paper cups. You’re supposed to get 10 ounces of coffee, but the amount varies slightly from cup to cup. Here are the amounts measured in a random sample of 20 cups. Is there evidence that the machine is shortchanging customers? (You may assume that the number of ounces dispensed in normally distributed)
9.9 , 9.7 ,10.0 ,10.1 , 9.9 , 9.6 , 9.8 , 9.8 , 10.0 , 9.5 ,10.1 , 9.9 , 9.6 , 10.2 , 9.8 , 10.0 , 9.9 , 9.5 , 9.9 , 9.7
a) Find a 95% confidence interval for the number of ounces dispensed by the machine.
b) Write a sentence giving your results in the context of the problem.
c) What does 95% confidence mean in this problem?
d) Does your confidence interval suggest that the company is or is not short-changing their customers? Explain
The mean of the sample data is 9.91 ounces and the standard deviation is 0.16 ounces.
To find the 95% confidence interval, we need to calculate the mean and standard deviation of the sample data. The 95% confidence interval can then be calculated as the mean ± 1.96 times the standard deviation, which is (9.59, 10.23) ounces.
b) The 95% confidence interval for the number of ounces dispensed by the machine is (9.59, 10.23) ounces.
c) 95% confidence means that if the same experiment were to be repeated 100 times, 95 of the confidence intervals would contain the true mean.
d) The confidence interval does not suggest that the company is short-changing their customers because it includes 10 ounces, which is the expected amount of coffee to be dispensed.
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which of the following refers to a statement that says that a change in one variable tends to follow or be associated with a change in another variable?
Correlation: A correlation is a statement that suggests there is a relationship between two variables, where a change in one variable tends to follow or be associated with a change in another variable.
A correlation is a statement that suggests there is a relationship between two variables. It does not necessarily mean that a change in one variable will cause a change in the other variable, but that a change in one tends to follow or be associated with a change in the other. For example, a correlation could be made between the amount of rainfall a region receives and the number of plants that are able to grow there. If the rainfall increases, then the number of plants that can grow in the region is likely to increase as well. A correlation can be either positive or negative, with a positive correlation meaning that an increase in one variable will likely result in an increase in the other, and a negative correlation meaning that an increase in one variable will likely result in a decrease in the other. Correlation can be used to make predictions, but should not be confused with causation, as correlation does not necessarily imply causation.
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The complete question: which of the following refers to a statement that there is a relationship between two variables that can change in one variable tends to follow or be associated with a change in another variable?
How do you express area in square feet algebraically
Length (in ft) x Width (in ft) = area in sq. ft
Hope this helps
I'm not good at math so I got this from my notes :)
If it doesn't help then it was worth an attempt...
You invest $1,200 that is compounded continuously at 9% for 10 years. What is the equation you use?
Answer:
FV = $1,200 * e^(0.09*10)
Step-by-step explanation:
The equation used to calculate the future value of an investment compounded continuously is:
FV = PV * e^(r*t)
where:
FV = future value
PV = present value (initial investment) = $1,200
r = annual interest rate (9% = 0.09)
t = number of years (10 years)
So, the future value of the investment would be:
FV = $1,200 * e^(0.09*10)
The sports bar owner runs a regression to test whether there is a relationship between Red Sox away games and daily revenue. Which of the following statements about the regression output is true? SELECT ALL THAT APPLY.
A. The average daily revenue for days when the Red Sox do not play away is $1,768.32.
B. The average daily revenue for days when the Red Sox play away is $1,768.32.
C. The average daily revenue for days when the Red Sox play away is $2,264.57.
D. The average daily revenue for days when the Red Sox do not play away is $1,272.07.
E. On average, the bar’s revenue is $496.25 higher on days when the Red Sox play away than on days when they do not.
B and E are true.The regression output can be used to determine whether there is a relationship between Red Sox away games and daily revenue.
The output can also be used to calculate the average daily revenue for each scenario.
For the scenario where the Red Sox do not play away, the output will give the average daily revenue, which is $1,768.32. So, statement A is true.
For the scenario where the Red Sox play away, the output will give the average daily revenue, which is $2,264.57. So, statement B is true.
For the scenario where the Red Sox do not play away, the output will also give the average daily revenue, which is $1,272.07. So, statement D is false.
Finally, the output can be used to calculate the difference between the average daily revenue when the Red Sox play away and when they do not, which is $496.25. So, statement E is true.
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For each problem, draw 2 triangles that have the listed properties. Try to make them as different as possible.
In a single triangle, there is a 40-degree and a 60-degree angle.
What is meant by triangles?A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees.
Triangles of the scalene, isosceles, and equilateral varieties differ from one another in terms of side length. The triangle is a scalene triangle if the lengths of the three sides are all different. An isosceles triangle is one with all three sides having equal lengths.
A 40-degree and a 60-degree angle are both present in one triangle. three for the side opposite the 40-degree angle, x for the side opposite the 60-degree angle, and six for the third side. A 40 degree angle and an 80 degree angle are present in the second triangle. The third side has a length of 8, the side opposite the 80-degree angle has a length of y, and the side opposite the 40-degree angle has a length of 5.
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estimated work cost [it is a time-dependent variable cost related to manpower project resources and the time they are utilized. equipment when associate with time usage (i.e., hourly rentals) is also classified as work.]
The total estimated work cost for the project would be $5200 ($5000 + $200).
The formula for calculating the estimated work cost for a project is C = P x T, where C is the estimated cost, P is the hourly rate of the personnel and T is the total amount of time spent working on the project. For example, if the hourly rate of a project manager is $50 and they work 100 hours on the project, the estimated work cost would be $5000 (50 x 100). In addition, any equipment that is used on an hourly rental basis should also be included in the estimated work cost calculation. For example, if a piece of equipment is used for 10 hours at a rate of $20 per hour, the estimated cost for this equipment would be $200 (20 x 10). Therefore, the total estimated work cost for the project would be $5200 ($5000 + $200).
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methods for solving systems of linear equations
( graphing )
how to graph
Y= 2x+6
Y=2x+2
locate the point of the intersection of the two lines
( , ) ?
Answer: imma be honnest im just trying to get points rn.
Step-by-step explanation: i have no idea but thank you for your time reading my nonescence.
There are integers b, c for which both roots of the polynomial x^2-x-1 are also roots of the polynomial x^5-bx-c. Determine the product bc.
It is discovered that the phrase under the division symbol is 3x2 - (b - 2)x - c, meaning that b = 5 and c = 3.
find the roots of x2 - x - 1 = 0
---> Using the quadratic formula, the roots are [ 1 + sqrt(5) ] / 2 and [ 1 + sqrt(5) ] / 2.
Placing these values into the equation x5 - bx - c = 0, we get:
x = [ 1 + sqrt(5) ] / 2 ---> ( [ 1 + sqrt(5) ] / 2 )5 - b( [ 1 + sqrt(5) ] / 2 ) - c = 0
---> [ 176 + 80sqrt(5) ] / 32 - ( [ 1 + sqrt(5) ] / 2 )b - c = 0
multiplying by 32 ---> 176 + 80sqrt(5) - 16b - 16sqrt(5)b - 32c = 0
Using the same steps for x = [ 1 - sqrt(5) ] / 2 , we get: 176 - 80sqrt(5) - 16b + 16sqrt(5)b - 32c = 0
Now, let's combine these two results: 176 + 80sqrt(5) - 16b - 16sqrt(5)b - 32c = 0
176 - 80sqrt(5) - 16b + 16sqrt(5)b - 32c = 0
Subtract the lower equation from the upper: 160sqrt(5) - 32sqrt(5)b = 0 ---> 160sqrt(5) = 32sqrt(5)b ---> b = 5
Now, substitute this value for b into 176 + 80sqrt(5) - 16b - 16sqrt(5)b - 32c = 0
--->176 + 80sqrt(5) - 16(5) - 16sqrt(5)(5) - 32c = 0
--->176 + 80sqrt(5) - 80 - 80sqrt(5) - 32c = 0
--->96 - 32c = 0
--->c = 3
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the following purchase is made at each store: 6 pounds of sugar, 3 cans of peaches, 2 pounds of chicken, and 5 loaves of bread. use matrix multiplication to find the total bill at each store. you may leave decimal answers in this problem. interpret the solution with context to the application.
The total cost of the items purchased at each store is $68, $52, and $72 respectively.
The total bill at each store can be found by using matrix multiplication. We will create a matrix of the costs of each item, and then multiply it by a matrix of the amounts of each item purchased. The resulting matrix will give us the total cost of the items purchased.
Let x be the matrix of costs per item:
x = [[5, 2.5, 2, 3],
[4, 2.75, 1.5, 2],
[6, 3, 1.75, 3.5]]
Let y be the matrix of amounts of items purchased:
y = [[6, 3, 2, 5]]
We can then find the total cost at each store by multiplying x and y together:
xy = [[68, 36.75, 29, 45.5],
[52, 28.25, 21, 30],
[72, 40, 33.5, 52.5]]
Interpreting the solution with context to the application, we can see that the total cost of the items purchased at each store is $68, $52, and $72 respectively.
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scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 24 laboratory rats. a 95% confidence inter- val for the mean blood cholesterol level m is 80.2 to 89.8. which of the following would cause the most worry about the validity of this interval? (a) There is a clear outlier in the data.
(b) A stemplot of the data shows a mild right skew.
(c) You do not know the population standard deviation �
.
(d) The population distribution is not exactly Normal.
(e) None of these would be a problem because the t procedures are robust.
